A particle is projected up an inclined plane of inclination β at an elevation α to the horizontal. Find the ratio between tan⁡α and tan⁡β, if the particle strikes the plane horizontally.

T=2usin⁡(α−β)gcos⁡β             …(i)Now we shall consider the motion of particle along OA. When the particle strikes the plane horizontally In this case, t=2usin⁡(α−β)gcos⁡βand 0=usin⁡α−gtusin⁡α=g2usin⁡(α−β)gcos⁡β2tan⁡β=tan⁡α⇒tan⁡α:tan⁡β=2